Four-point correlation function of stress-energy tensors in N=4 superconformal theories

TL;DR

This work derives an explicit, symmetry-driven expression for the four-point function of the stress-energy tensor in four-dimensional $\mathcal{N}=4$ superconformal theory, showing that SUSY reduces the functional freedom to a single scalar function. It introduces a master formula via $\mathcal{N}=4$ Ward identities and an auxiliary-spinor formalism, yielding a compact, derivative-based representation for the anomalous part of the $\langle TT TT\rangle$ correlator. The analysis extends systematically to four-point functions involving other conserved currents and demonstrates that energy-energy correlations (EEC) are universal across scalar, vector, and tensor sources, governed by a universal function $\mathcal{F}(\chi)$. The results connect to dual conformal invariants found in scattering amplitudes, offer predictions at strong coupling via AdS/CFT, and provide a framework for computing a broad class of observables using symmetry alone. Overall, the paper highlights a remarkable simplification of complex four-point structures and the universality of energy-flow observables in $\mathcal{N}=4$ SCFT.

Abstract

We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.